
Heisenberg's uncertainty principle in harmonic analysis is of central importance in time-frequency analysis as is it provides a lower bound for optimal simultaneous resolution in the time and frequency domains (see [1]}). This principle has been extended to different time-frequency transforms and several other versions of the uncertainty principle have been investigated from time to time. For instance, Beckner [2]} obtained a logarithmic version of the uncertainty principle by using a sharp form of Pitt's inequality and showed that this version yields the classical Heisenberg's inequality by virtue of Jensen's inequality. In this Section, we shall establish an analogue of the well-known Heisenberg's uncertainty inequality and the corresponding logarithmic version for the quaternion linear canonical wavelet transform as defined by (3.9). We first prove the following lemma.
